How Odd...

Odd is a particularly Norwegian name for boys. It stands to reason that it is not much used in English-speaking countries, but even in Denmark and Sweden it is not much used. The name has very old roots, however. It was used in name combinations for both males and females, probably as a symbolic protection, as names back then were supposed to be strong and protective. To the old Norsemen the word meant spear or any pointy end, and in modern Norwegian it is still understood as the sharp end of something.

Many old Odd combinations have been kept in use, but Odd has also become a name on its own, as well as part of numerous new combinations. From the 1920s to the 1940s the name featured in the top 5 lists of the most popular names given to boys, and although it's slightly rarer today, it is still a common name.

Odd can be a pretty difficult name to have outside of Norway, unless you don't mind being odd, of course.

One man by that name who had moved to America at a young age found it quite insufferable after some time, and after hearing one joke too many he exploded: Enough laughs about my odd name! When I die, my headstone shall be blank - nobody shall joke about my name again!

Sooner rather than later, the man died and his friends rembered his words with deep regret. They buried him and placed a totally blank headstone at his grave.

But whenever anyone walked past it, they would look at the empty headstone and say: "Hmm, that's odd!"

A number (more specifically, an integer) is odd if it is not congruent to zero, modulo 2. In other words, when you divide the number by two, you will get some-number-and-a-half (not a whole number), or a number x is odd if (and only if) it can be written as x = 2n + 1 for some integer n.

If the domains of f and h overlap, then f(x) + h(x) is not even, but it is not odd either unless h(x) = 0

A polynomial of x is odd if the power of x in every term is an odd number. (Note that (-x)2n + 1 = (-x)*(-x)2n = (-1)*(x)*(x)2n = -((x)2n + 1); every term in an odd polynomial is an odd function.)

Odd polynomials are odd functions, and continuous odd functions can be approximated to any desired accuracy by odd polynomials. However, there are functions which are neither even nor odd, and there are polynomials which are neither even nor odd. This is different than for integers; every integer is either even or odd. (In fact, the function f(x) = 0 is both odd and even, thanks to ariels for setting this straight for me.)

BrianShader reminds me: You might like to point out that any function can be written as an even function plus an odd function.